Mr Trump broke a long-held tradition by not releasing his paperwork during his presidential campaign.
His critics want to know who he has been dealing with and if there are any conflicts of interest.
At least 21 people were arrested in Berkeley, California, in clashes between Trump opponents and supporters.
There is no law requiring presidents to release their tax returns, but Mr Trump has found himself under public pressure and some information from a 2005 tax return was leaked to the media last month.
The protests were timed to coincide with the traditional mid-April deadline for Americans to file their tax returns.
"I think it is critical we know about his investments, his donations and any entanglements he has," said one protester, Chuck Wash, at a march in Washington DC.
The idea for the themed march came from law professor Jennifer Taub, who was angered when presidential adviser Kellyanne Conway said President Trump would not be releasing his tax returns because "people don't care".
In January, Ms Taub tweeted of the need for a nationwide protest to show the president that many people do care.
The idea quickly caught on.
"I wanted to express myself and never in my wildest dreams did I think I would be standing here today, seeing this idea that I tweeted out in January come to life," she told the BBC at the Washington DC march.
Ms Taub said the march had broader aims than just wanting to see the president's paperwork.
"This is also about having a tax system that is fair," she said. "Both in terms of making sure everyone pays their fair share and also in taking public resources - our taxes - and spending them on things that make everyone flourish."
She said less should be spent on wars, and more should go to public service television and the Meals on Wheels programme, which Mr Trump has made funding cuts to in the first months of his presidency.
Congresswoman Maxine Waters, a Democrat from California, was also at the march in Washington DC.
She said the Trump administration has a "huge" transparency problem.
"He [Trump] talked about draining the swamp and making everything transparent. He lied again," said Ms Waters.
She also criticised Friday's announcement that President Donald Trump will not release the logs of those who visit the White House.
The White House cited "grave national security risks and privacy concerns" as the reason for its decision, reversing former President Barack Obama's voluntary disclosure policy.
Participants used the hashtag #showusyourtaxes to share their images on social media.
President Trump's supporters have also gone online to express their support for the president.
One Twitter user accused protesters of "flogging a dead horse" and many said they had no interest in seeing the returns.
Separately, more than a dozen people were arrested in Berkeley, California, after supporters of Mr Trump clashed with anti-fascist demonstrators at a free speech rally, police said.
Several people were injured when fighting broke out at a park in the city as opponents and supporters of the US president met on the streets during Saturday's protests, according to CNN.
Footage shared on social media showed crowds of people throwing items at one another and demonstrators being attacked with what appeared to be chemical sprays and makeshift weapons.
The incident occurred after hundreds of anti-Trump protesters staged a counter-rally alongside an event billed as a "Patriots Day free speech rally and picnic", organised by the president's supporters.
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